Search · four archives
Search · four archives
23 papers · ranked by Valyu relevance
Bethany Lusch, J. Nathan Kutz, Steven L. Brunton
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear has the potential to enable nonlinear prediction, estimation, and control using linear theory. The Koopman operator is a leading data-driven embedding, and its eigenfunctions provide intrinsic coordinates that globally…
Julia Lieb, Joachim Rosenthal
It is well known that there is a correspondence between convolutional codes and discrete-time linear systems over finite fields. In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. In this kind of channel…
Parsa Veysi, mohsen adeli, Nayerosadat Peirov Naziri, Ehsan Adeli
—This research paper presents a detailed and approachable exploration of the Linear Kalman Filter (LKF) as a pivotal tool in the fusion of data originating from multiple sensors, providing a nuanced understanding of its capabilities in managing the intricacies of dynamic system estimations and predictions. The Kalman…
Ion Victor Gosea, Serkan Gugercin
We extend the Adaptive Antoulas-Anderson (AAA) algorithm to develop a data-driven modeling framework for linear systems with quadratic output (LQO). Such systems are characterized by two transfer functions: one corresponding to the linear part of the output and another one to the quadratic part. We first establish the…
Ramachandran Anantharaman, Virendra Sule
Given a discrete dynamical system defined by a map in a vector space over a finite field called Finite State Systems (FSS), a dual linear system over the space of functions on the state space is constructed using the dual map. This system constitutes the well known Koopman linear system framework of dynamical systems…
Roger A. Horn, Vladimir V. Sergeichuk
This is a survey article for Handbook of Linear Algebra, 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The notion of quiver representations is extended to representations of mixed graphs, which…
Nikolai Krivulin
A linear vector equation is considered defined in terms of idempotent mathematics. To solve the equation, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces and reduces the solution of the equation to that of a tropical optimization problem. Based on the…
Václav Skala
A solution of linear systems of equations Ax=b and Ax=0 is a vital part of many computational packages. This paper presents a novel formulation based on the projective extension of the Euclidean space using the outer product (extended cross-product). This approach enables to solve the both cases, i.e. Ax=b and Ax=0 The…
Peter J. Gawthrop, Michael Pan
The sensitivity of systems biology models to parameter variation can give insights into which parameters are most important for physiological function, and also direct efforts to estimate parameters. However, in general, kinetic models of biochemical systems do not remain thermodynamically consistent after perturbing…
Ryotaro Sakata, Tatsuya Oshima, Shin Kawai, Triet Nguyen-Van
This paper attempts to extend the concept of the equilibrium point to what is called equilibrium space, which can adapt to a system in which there exists an infinite number of equilibrium points. In the context of Lyapunov’s linearization method extended for the equilibrium space, this paper proposes a pseudo…
Rodrigo Osuna-Orozco, Edward Castillo, Kameron Decker Harris, Samantha R. Santacruz
Large-scale recordings of neural activity over broad anatomical areas with high spatial and temporal resolution are increasingly common in modern experimental neuroscience. Recently, recurrent switching dynamical systems have been used to tackle the scale and complexity of these data. However, an important challenge…
Fateme Olia, Shaban Ghalandarzadeh, Amirhossein Amiraslani, Sedighe Jamshidvand
'Sedighe Jamshidvand'] Abstract. In this paper, we introduce and analyze a normalization method for solving a system of linear equations over tropical semirings. We use a normalization method to construct an associated normalized matrix, which gives a technique for solving the system. If solutions exist, the method can…
Hannes Löwe, Andreas Kremling, Alberto Marin-Sanguino
The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much…
Osama Abdelaleim, Arun Prakash, Ayhan Irfanoglu, Veljko Milutinovic
—Accelerating the solution of linear systems of equations is critical due to their central role in numerous applications, such as scientific simulations, data analytics, and machine learning. This paper presents a general-purpose analog direct solver circuit designed to accelerate the solution of positive definite…
Arturo Tozzi
A wide range of biological and evolutionary processes is determined not merely by the occurrence of specific events, but by the exact order in which those events unfold. Gene regulation, developmental pathways, metabolic cascades and genetic evolution often display non-commutative behaviour, in which reversing the…
Ehsanoddin Ghorbanichemazkati, Amro M. Farid
Graphs for System-of-Systems Engineering Applications Authors: ['Ehsanoddin Ghorbanichemazkati' 'Amro M. Farid'] In the 20th century, individual technology products like the generator, telephone, and automobile were connected to form many of the large-scale, complex, infrastructure networks we know today: the power…
Authors not listed
Rapid and robust simulation of chemical processes is critical to conduct process design, optimization, techno-economic analysis, and sustainability analysis. Yet, efficiently solving simulation models remains a challenge due to the highly coupled and nonlinear nature of the underlying algebraic equations that capture…
Itai Dattner, Harold Ship, Eberhard O. Voit
Nonlinear dynamic models are widely used for characterizing processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data collected via high-throughput experiments using methods from molecular biology. While these data are…
Authors not listed
We present a vector-based method to balance chemical reactions. The algorithm builds candidates in a deterministic way, removes duplicates, and always prints coefficients in the lowest whole-number form. For redox cases, electrons and protons/hydroxide are treated explicitly, so both mass and charge are balanced. We…
Ismaila Muhammed, Dimitris M. Manias, Dimitris A. Goussis, Haralampos Hatzikirou
Biomedical systems inherently exhibit multi-scale dynamics, making accurate system identification particularly challenging due to the complexity of capturing a wide time scale spectrum. Traditional methods capable of addressing this issue rely on explicit equations, limiting their applicability in cases where only…
Ayush Pandey, Richard M. Murray
We present an automated model reduction algorithm that uses quasi-steady state approximation based reduction to minimize the error between the desired outputs. Additionally, the algorithm minimizes the sensitivity of the error with respect to parameters to ensure robust performance of the reduced model in the presence…
Oskar Weser, Björn Hein Hanke, Ricardo Mata
In this work, we present a fully automated method for the construction of chemically meaningful sets of non-redundant internal coordinates (also commonly denoted as Z-matrices) from the cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to…
Authors not listed
Quantum state tomography has been widely used to reconstruct the quantum state of a system from a set of informationally-complete measurements. Obtaining enough information about, e.g., the wavefunction of a molecule allows its complete characterization. On the other hand, deep learning models for molecular property…